On the formal equivalence of the TAP and thermodynamic methods in the SK model

Andrea Cavagna 1, Irene Giardina 1, Giorgio Parisi 1, Marc Mézard 2

Journal of Physics A 36 (2003) 1175-1194

We revisit two classic Thouless-Anderson-Palmer (TAP) studies of the Sherrington-Kirkpatrick model [Bray A J and Moore M A 1980 J. Phys. C 13, L469; De Dominicis C and Young A P, 1983 J. Phys. A 16, 2063]. By using the Becchi-Rouet-Stora-Tyutin (BRST) supersymmetry, we prove the general equivalence of TAP and replica partition functions, and show that the annealed calculation of the TAP complexity is formally identical to the quenched thermodynamic calculation of the free energy at one step level of replica symmetry breaking. The complexity we obtain by means of the BRST symmetry turns out to be considerably smaller than the previous non-symmetric value.

  • 1. Center for Statistical Mechanics and Complexity, INFM Roma 'La Sapienza' and Dipartimento di Fisica,
    Università degli studi di Roma I - La Sapienza
  • 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud